ADVANCED: Randomization

GVPT399F: Power, Politics, and Data

Randomization

  • Last session, we randomly assigned 1,000 hypothetical people to two different groups

  • Testing whether randomization helps us create two roughly identical groups prior to treatment

  • You now have a lot of the R code needed to replicate that analysis

Creating our group of 1,000 people

Imagine we have a group of 1,000 individuals. We know the following about them:

  • Height

  • Weight

  • Eye colour

Creating our group of 1,000 people

group_df <- tibble(
  id = 1:1000,
  height = rnorm(1000, 170, 6),
  weight = rnorm(1000, 80, 10),
  eye_colour = sample(c("Blue", "Green", "Brown", "Grey"), 
                      1000, 
                      replace = T)
)

group_df
# A tibble: 1,000 × 4
      id height weight eye_colour
   <int>  <dbl>  <dbl> <chr>     
 1     1   169.   58.8 Grey      
 2     2   172.  104.  Grey      
 3     3   173.   93.7 Grey      
 4     4   165.   77.6 Brown     
 5     5   169.   65.3 Green     
 6     6   161.   85.1 Grey      
 7     7   180.   73.4 Grey      
 8     8   172.   71.3 Green     
 9     9   167.   81.1 Green     
10    10   167.   75.1 Green     
# ℹ 990 more rows

The Normal distribution

ggplot() + 
  geom_density(aes(x = rnorm(n = 1e6, mean = 0, sd = 1))) + 
  theme_minimal()

Random sampling from the Normal distribution

I can take a random sample of n values from a Normal distribution centered at some mean with a specific standard deviation.

  • By default, rnorm() takes a mean of 0 and a standard deviation of 1

  • The following code takes 1,000 random samples from that default Normal distribution

Random sampling from the Normal distribution

rnorm(n = 1000, mean = 0, sd = 1)
   [1]  0.376165037 -2.740614049 -1.458463698 -2.033406631  0.642322324
   [6] -0.833443691 -0.039488687 -0.216271009 -0.475838339 -0.933089546
  [11] -0.373974684  1.195809061 -0.070363351  0.991856775  0.358718920
  [16]  1.839828939  0.595415534 -0.111405213 -0.114668630 -2.403735625
  [21]  0.333133629 -0.606346864  0.551008113 -0.956050008 -0.522876687
  [26] -0.493050293 -1.207251680  0.606774088  1.383250259  0.019693607
  [31]  2.341265610  1.748358459 -1.132099208  0.388150716 -1.435686737
  [36]  1.416472234 -0.602200493 -0.179620113 -0.857630588 -0.188732939
  [41]  2.344814025  0.845930647  0.190338694 -1.328667924 -2.010576764
  [46] -1.090722367  0.599521832  0.796349020 -0.505176638 -0.008549396
  [51]  0.094122896  1.843196899  1.742627790  0.655090159  0.874489785
  [56] -0.408738568 -0.361156584 -1.103851637 -0.330050287  0.632440080
  [61]  0.218280317  0.109883833 -1.334873061 -0.988655858  0.601432295
  [66]  0.521925167  0.078854162 -0.163329882  0.043441389 -1.931155221
  [71] -0.483929571 -0.400972675 -0.675587573  1.594918504  1.235875387
  [76]  0.256475344 -0.556696586 -1.362233034 -0.112319762 -0.322071773
  [81] -1.546850587  0.663694687 -0.236454318  1.451134567 -0.865863453
  [86]  0.808311420  0.721125107  0.661951278 -0.348275150 -0.026418036
  [91] -0.242214776  0.292849230  0.996720393 -0.439261222 -0.871100038
  [96] -0.668951439  2.299768666 -0.693834788 -1.376695816 -0.107321143
 [101] -0.380496989 -0.694101218 -0.960044729 -1.259149527 -1.047414039
 [106] -0.832734076  0.440912173 -0.210556784 -0.326976691  1.028050172
 [111] -2.059201525 -2.219458893  1.713168254  0.376644452  1.604641875
 [116] -1.152088633  0.399052829  0.381648101 -1.330088991 -0.071793906
 [121] -0.093456558 -0.467989168  1.729063439 -0.221463779  1.177171740
 [126]  0.515012254  0.886688337 -0.585866528 -0.687130301 -0.945012894
 [131]  0.886831369 -0.677727593 -0.932346466 -1.414058371 -0.230472094
 [136]  1.275557029 -2.619574787 -1.040850628  0.155124253 -0.674496418
 [141]  0.938958478  1.880567764  1.123186357 -1.125705192  0.903548662
 [146]  0.674797254  0.053547896  0.699780062 -0.135372746 -1.076969867
 [151] -2.032594094 -1.633382165 -1.782050541  0.314256728  0.251253498
 [156] -0.940663372 -1.131012851  1.306285748 -0.733338541  2.275433892
 [161] -1.656881065  0.300560019  0.486759286  0.185618851 -1.064256406
 [166]  1.080054194 -0.942275031  1.822142226 -0.870702669 -1.204506750
 [171] -0.456489259 -0.098849788  1.210668911  1.846484272  0.449823016
 [176]  0.618508507  0.262351176 -0.612687983  0.447891041  0.580008006
 [181]  1.824237132 -0.960986558 -0.371166444  0.495071923  0.754523659
 [186] -0.683574001  0.719659686  1.896203007 -1.926535238 -1.199631541
 [191]  1.378210348  1.382221041 -0.879704720 -0.159750674  0.580716084
 [196] -0.007241833  0.264678882  1.162209753 -1.821669478 -0.404152857
 [201] -1.873360061 -0.323491927  1.887690404  0.423126991 -0.463009788
 [206]  0.396237644  1.040945741 -0.648804757 -0.067221462  1.551031830
 [211]  2.294251973  1.579375458 -0.587143934 -1.313870667 -1.312315187
 [216] -0.222468868 -0.370389394 -0.404407382 -0.306960217 -1.835523080
 [221] -0.769958591  0.790086778  0.260309446  0.471261371 -1.350295465
 [226] -0.618822726 -0.319227099 -0.091335884  1.944043359 -0.929931698
 [231] -0.757936578 -1.456129895  0.711225084 -0.203186607 -0.889901203
 [236]  1.125573450  1.088216927 -0.358737694  0.562414555 -0.851641627
 [241] -1.304327842  0.530640766 -0.309724909 -2.221303215 -0.236250008
 [246] -0.501758531 -1.298597392  1.064944573  0.363232736  1.032155288
 [251] -0.388493459 -0.681374144 -0.961544546  0.163775146 -1.023419899
 [256]  0.297111268  0.455755603 -0.455819301 -1.323479359  0.143375246
 [261]  0.115205298  0.298701214  0.236744966 -0.519846282  0.200747651
 [266] -0.691442325 -0.104099036  0.167562566  2.048988749  1.214219019
 [271]  0.997482023 -0.403966038 -0.770355844  0.163190670 -1.618931670
 [276] -1.547371789 -0.702249092 -1.504556871 -1.281757674 -0.420189981
 [281] -0.437837452  1.503314151 -1.280587914 -1.561024635  0.491205439
 [286]  0.138916164  0.219607234 -1.224206807  0.226683312 -0.887022622
 [291]  1.933581287 -0.977398426 -0.380441337  0.967294718 -0.058625799
 [296] -0.001330943 -1.184045452 -0.014855786 -0.398086159  0.314296243
 [301] -1.117379065 -0.600853356  0.779670155  0.589546302  0.130045806
 [306]  1.352192881 -1.745088408  1.205331621 -0.208952483  0.851714369
 [311]  1.897890156 -0.380919108  1.317520712 -1.930410235  1.601977111
 [316] -0.859125136  1.259101836 -0.820635457  0.105678997 -0.254282265
 [321] -0.407995217 -0.082085748 -0.614449460 -0.168129396  1.105946240
 [326] -1.124281278  0.186377597 -0.665337381  2.119038531 -0.170945022
 [331]  0.511785791 -0.211725228 -0.819785967 -1.411224429  1.709001643
 [336]  0.056243221  1.109628253 -1.473977815 -0.117602084 -0.388211289
 [341] -0.876652037 -1.977751856 -0.346266436 -0.217939553  2.095984493
 [346] -1.510358888 -0.714179342 -1.108805986 -1.530041326 -0.937372691
 [351] -1.059249641 -0.789145872 -0.916376949 -1.992374612  0.476336406
 [356] -0.763413655  1.150163058 -0.753537239  0.862157025 -1.325787683
 [361] -0.005505332  0.051373522 -0.346697829 -0.198059292  1.139728809
 [366]  0.543291115 -1.176512533  0.565916299 -1.430268158 -0.195639145
 [371] -0.054899901 -1.544876122 -1.294983369 -0.267988423 -0.235583842
 [376]  1.587597865  1.387176055 -0.034539812 -0.249048366 -0.011987682
 [381]  0.033793763 -1.234686782  0.567914034 -1.310049788 -0.329538196
 [386] -1.462840565  2.258760445 -1.486103195 -0.510356458  2.463099873
 [391] -0.439424063  0.935261718  1.000352680 -1.285504676 -0.846941084
 [396] -2.298145594  0.153694528 -0.376208814  0.130813689 -1.632509642
 [401] -0.921933584 -1.393319823  0.828604059 -1.055682194 -0.809058438
 [406]  1.687335434 -0.806400579 -0.082532214  0.177941237 -0.572846052
 [411] -1.666598275 -2.393002740  0.476894472 -0.427989468 -0.885109945
 [416]  1.005108674  0.041337304 -0.660890270  0.075950674 -0.421452020
 [421] -1.549932679 -0.919825449 -0.508904463 -0.217134625 -0.167576597
 [426]  0.844102521  0.091477004  0.264807569 -0.580979393 -0.432445716
 [431] -2.132341520 -0.092715063  1.918009561 -0.116460999  0.547205093
 [436] -0.679378551 -0.199067994 -0.186132291  0.602788763 -0.416066041
 [441] -0.313121930 -0.880484915 -0.198625196  0.592122424  0.239654889
 [446] -1.433317653  0.380279582  1.102428968 -0.520660551 -0.167087821
 [451]  0.024200348  0.893916592 -0.162674220  1.047036349  0.419661662
 [456]  0.064252996 -0.305519531  0.440940566 -0.583059725 -0.280263039
 [461] -1.291141242 -0.613114034  0.666758673  0.214392818  0.342965582
 [466]  1.083280258  1.052957415  1.111115467 -1.267738327 -0.480236523
 [471] -0.472055738 -1.397164392 -1.148958796  0.132286790 -2.608167980
 [476]  0.878088715 -1.729217413  1.230488947  0.487016040  1.709191431
 [481] -2.536326657  0.629946271 -0.131384562  0.138303633  2.037524950
 [486]  0.887946734 -1.788592495  0.631065766 -1.077109667 -0.309286946
 [491]  0.431436953 -0.986471564 -1.534790725 -0.789323454 -1.177555454
 [496]  0.214592668  0.534670821 -0.818179056  0.574328947 -0.227192560
 [501]  0.220746678 -0.682618157  0.441359174  0.350013620  0.187241333
 [506] -1.456388938 -0.458079644  0.263145643 -0.705141707  1.186955322
 [511]  0.148341359 -1.117525862  1.866206194  1.274561128  1.346855440
 [516]  1.324529732  0.322274468 -0.703737217 -0.408532737  1.034881431
 [521]  0.537482811 -1.299021267 -0.083436558 -0.823560508 -0.740476982
 [526]  1.499110664 -0.486754232  1.145245155  0.778935411 -1.557606724
 [531] -0.219866504  0.512739387 -1.379670066 -1.469470342 -0.896186284
 [536]  0.192740431  1.226697813 -1.063813922  0.177487101 -0.229284944
 [541]  0.515931883 -1.386003838  2.139479721  1.436039850  0.349578183
 [546] -0.428236843  0.894333718 -0.179095270  1.043862728 -1.438936540
 [551]  0.586774739  1.944848814  1.851416983  0.022810307  1.636223903
 [556] -0.151048005  1.968595163  0.596417946  0.229870516  0.364992777
 [561] -1.177552541  0.428048448  2.244464941 -0.126132219 -1.296797531
 [566] -0.025442598 -0.617203351 -0.615851865  1.769396006 -0.335980202
 [571]  1.747894664 -2.261716438  0.818727615  0.436905457 -2.485164142
 [576]  1.323976615 -0.431859355 -1.193383819  0.217776829  1.014815805
 [581]  0.094956897 -0.754231825 -0.400262474 -1.059002079 -0.492970703
 [586]  0.516874654 -0.977914234  1.087320800 -1.936133615  1.533196534
 [591] -1.180536376  0.128624482 -0.092664843 -1.129151716 -1.261534018
 [596]  2.485927620  1.066576748  0.799412991  1.908184843 -1.382708265
 [601] -0.585319559 -0.575596110  2.278979991 -1.206463328  0.464362742
 [606] -0.061037836  0.229798104 -1.507683337  0.034313048  0.662528917
 [611]  1.794553076  0.430043969 -0.041992548 -0.374099257 -0.388628512
 [616]  0.837847204 -0.732227927  0.792564682 -0.586843139 -0.688756141
 [621] -1.588247364  0.111529881  0.529728702  0.786019406  0.693162036
 [626] -0.232396566  0.349082311  0.785661020 -0.224240145  0.384412424
 [631]  1.049876599  1.191022518  0.636929729  0.819891024  0.582858150
 [636]  0.443667688 -0.819297596  0.604219371  0.750111854  0.634520488
 [641]  0.747099273  0.087044365 -1.063094372 -1.059391569 -0.070862726
 [646] -0.178523907 -0.120228225 -0.430461461 -0.241569449 -0.046016299
 [651]  0.361298911 -0.351854735 -1.006312251 -0.949800973 -1.531030016
 [656]  0.044524246  1.224481884 -0.070537530 -1.569771605  1.454090378
 [661]  0.621972667  0.663599702  0.882059167  0.172682605 -0.408635657
 [666]  1.062958513 -1.649770154 -0.947289361  0.526619909  0.492723732
 [671]  1.290046431 -0.013943709 -0.427886650 -2.275893765  0.508538676
 [676]  0.109898601 -0.451230575 -2.321145342  0.152922857 -1.718581535
 [681] -0.377116059  0.591111943  0.798428980 -1.433129672  1.729366579
 [686]  0.486890453 -1.935790844  1.993641508 -0.865383042 -0.828675792
 [691]  0.260829767 -1.274631545 -0.049546925  0.555101657 -0.835872499
 [696]  2.471700563 -1.266859648 -0.466988502 -0.679579318 -0.191598792
 [701] -0.687122363  0.483547854  0.750896559  1.422892237  0.199096998
 [706]  0.697170069  1.732317666  0.267541034 -2.148979902 -1.820684046
 [711] -1.234623471 -1.415704680 -0.681981066  0.877442362  0.196744105
 [716] -0.012663366  0.699806864 -1.809449888  1.304150125  0.918325812
 [721]  0.252964917  1.628245669 -0.189715019 -0.358454746  0.546149377
 [726] -0.955184449  0.292588561 -1.215345481  0.572775712 -0.681060401
 [731]  1.250928722 -0.331781832 -0.520408383 -0.173838678  0.344779787
 [736]  0.386769312  0.999471042  1.569203179  0.633174642  0.773415693
 [741] -1.212160161  0.699504188 -0.891008781  0.011218427  0.150043605
 [746]  0.555627188  1.215338134 -0.288819416 -0.710237060 -1.345681185
 [751]  0.669511526 -1.276629517  0.890399609  0.001495167 -1.033242651
 [756]  0.507738478 -0.577532052  0.072945822 -0.531733456  0.716168323
 [761]  0.207056607  1.324022706 -0.951419756  0.689513618 -0.705200212
 [766]  0.413893929  0.193370594  1.987712925 -1.599235735 -0.682418194
 [771]  0.667068253 -0.351183636 -0.487276284 -0.830772772  1.032915707
 [776]  0.071881881 -0.578784053 -2.147498937  0.968015845 -1.471399929
 [781]  0.109831595 -1.292965372 -0.127711670  0.658486654 -0.371016349
 [786]  0.977845068 -0.102062043 -0.353557094  0.492293373 -2.122043932
 [791] -1.641021542 -0.262026959 -0.906452466  0.929641880  0.298837240
 [796]  1.127027817  0.644177507  1.958354715 -1.062967867 -1.748054407
 [801]  1.328701889 -1.527883779  1.309533952  0.506039929  0.546534924
 [806] -1.731067294 -0.375976262  0.289248202  0.910921581 -0.433145222
 [811] -0.447340357  0.018736855  0.819894452 -2.424743741  0.311618838
 [816] -0.805173910 -1.306186952 -0.633462111 -0.442861593 -0.885153086
 [821] -0.664092050  1.196216416 -0.309391614 -1.300826767  0.115950985
 [826] -0.141989353  0.344981203 -0.790221415  0.782894145  0.459606114
 [831]  0.338795617 -0.671077765 -1.691723596 -0.541218785 -0.398604108
 [836]  0.198451893 -0.214526846  0.285561245 -1.258069737 -1.698176792
 [841] -0.724327533 -0.448732446 -0.486108785  1.081173288 -0.321506010
 [846]  0.454942456  0.053354915  0.437885024 -0.485679313  0.939378927
 [851] -1.382919475  0.153917822 -1.317368545  2.649399151 -2.069947680
 [856]  0.326165063  0.770267233 -0.423234959  0.335093234  0.421088284
 [861] -1.902490138 -1.252875134  0.651824852  1.418472389  0.891193953
 [866]  1.662124018  1.004096340  0.242474163 -1.612776810 -0.670003756
 [871]  0.047991729  0.481248154 -0.941233992 -2.004662598  2.101547191
 [876] -0.372123391  0.496822553  0.949000228  0.293255305  0.251431367
 [881] -0.405463203  1.154754576 -0.421716460  0.187986139  0.245098581
 [886]  0.734010547 -0.477121081 -0.576075752 -0.880138821 -1.031710760
 [891] -0.254471817 -1.031567821 -2.487174224  1.271520644 -1.022119433
 [896] -1.640932612 -1.089054319 -0.360607386  0.245534067 -1.201844238
 [901] -0.737534926 -1.427591442 -0.277300120 -0.879242582 -0.392154049
 [906] -0.681700526  0.132203800 -0.068622509  0.748138329  0.208200835
 [911]  0.089096973 -1.079172310 -0.743312553  0.770652249 -2.143856861
 [916] -0.088033937  1.090276460 -0.959998790 -1.289753744 -1.551490295
 [921] -0.140583056 -0.382321864 -0.973479100  0.095595605  0.188068737
 [926]  0.290101984  0.053241600  1.007995489  0.087006939  0.926506024
 [931]  0.290684277  0.077469963 -1.338843268  0.325669285  0.118007209
 [936] -0.369067448 -0.217762847  0.998687964  0.291151058  0.718378853
 [941]  0.338724156  1.489952032  0.337812938 -0.433880695  0.210143726
 [946]  1.692462453  0.309064771 -1.765842731  1.612761872 -0.326556206
 [951]  0.116755371 -0.443078610  1.007732800  1.435745623 -0.464316404
 [956] -0.695366902  2.370443200  0.281167627 -0.630321189  0.659897206
 [961]  2.684826919  0.611889291 -0.444811666 -0.892663388  0.125696848
 [966]  0.458496356  1.009968801 -0.773032997  0.021146401 -0.018262618
 [971] -1.885471405 -0.952505054 -2.031235496  0.680568325  0.434324286
 [976]  1.583772773  0.709889977 -0.898031838  1.700382917 -1.113533104
 [981]  0.379511648 -1.010983932 -1.188268684  1.257125873  0.480864619
 [986]  2.322476951 -0.245785290 -0.614447544  0.087908795  1.030036099
 [991]  0.679165628  0.135120481  1.556539559  0.198242435 -0.472366994
 [996] -0.376743016  0.227984606 -0.461152371 -0.885703980  0.837801965

Random assignment using the Binomial Distribution

Remember, we then randomly assigned them to one of two groups: A or B.

  • I used random draws from the Binomial (read: binary or two) distribution to do this.

Random assignment using the Binomial Distribution

rbinom(n = 1000, size = 1, prob = 0.5)
   [1] 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 0 1 0 1 0 0 1 0 0 0 1 1 0 0 1 0 0 1 0
  [38] 0 1 0 1 1 0 0 0 0 1 0 1 0 0 0 1 0 1 0 1 0 0 0 0 1 0 0 1 1 1 0 1 0 1 1 0 0
  [75] 1 1 0 1 0 1 1 1 1 0 1 0 1 0 1 1 0 0 0 0 0 0 0 1 1 0 0 0 0 0 0 0 0 0 1 0 0
 [112] 0 1 1 0 1 1 1 0 1 0 1 1 0 0 1 0 0 1 1 0 0 0 1 1 1 1 0 0 0 1 0 1 1 0 0 1 0
 [149] 0 1 1 1 0 0 0 1 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 1 1 0 0 1 1 0 1 1 1 0 0 0
 [186] 0 0 1 1 1 1 0 1 1 1 0 0 1 0 0 0 1 1 1 0 1 0 1 1 1 0 1 1 0 0 0 1 1 1 0 0 1
 [223] 0 1 1 0 0 1 0 0 1 1 0 0 1 0 1 1 0 0 0 1 1 0 1 0 0 0 1 1 0 0 0 1 1 1 0 0 1
 [260] 1 0 0 1 1 1 1 0 0 1 0 0 1 0 1 1 0 1 1 0 1 0 1 0 1 1 1 1 0 0 1 0 1 0 0 0 0
 [297] 0 0 0 0 1 0 1 1 1 0 0 0 1 1 1 0 0 1 1 1 0 1 0 1 1 0 0 1 1 1 1 0 1 1 1 1 1
 [334] 1 0 0 1 0 1 1 0 0 1 0 0 0 1 0 1 1 0 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 1 1 0
 [371] 0 0 1 0 1 1 1 1 1 1 0 0 0 0 1 0 1 1 0 1 1 1 1 1 1 1 1 0 0 0 1 0 0 1 0 0 1
 [408] 1 1 0 1 0 1 0 1 0 0 0 0 1 1 0 0 1 0 1 0 1 1 0 1 1 0 0 1 1 0 1 1 0 1 1 1 1
 [445] 0 0 0 1 0 0 1 0 1 1 1 1 0 1 0 1 1 0 0 0 1 0 0 1 1 1 0 0 1 1 1 1 1 1 1 0 1
 [482] 0 1 0 0 0 0 1 0 1 1 0 1 0 1 0 0 0 0 0 0 0 0 0 1 0 1 0 0 0 1 0 1 0 0 0 1 1
 [519] 0 0 0 0 0 1 1 0 1 1 0 0 1 1 0 1 0 0 0 1 0 0 1 0 1 0 1 1 1 1 0 1 1 1 0 0 1
 [556] 0 0 0 0 0 0 1 1 1 1 1 1 1 1 1 1 1 0 1 0 0 0 1 0 1 0 1 0 0 1 1 0 0 1 0 1 0
 [593] 1 1 1 1 1 0 1 0 1 1 1 0 0 0 1 1 1 1 0 1 0 0 1 1 1 1 1 1 1 0 1 1 1 0 0 1 0
 [630] 0 1 1 1 0 0 1 0 0 1 0 0 0 0 1 0 0 0 1 1 1 0 0 1 1 0 1 1 0 0 1 0 0 0 0 1 0
 [667] 0 1 1 1 1 0 1 0 1 0 0 0 1 0 0 0 0 1 0 0 1 0 1 1 0 0 1 1 1 0 1 1 1 1 1 0 1
 [704] 1 1 1 1 0 1 0 1 0 1 0 1 1 1 1 0 0 1 0 0 0 0 0 1 0 1 1 1 0 1 1 1 1 1 0 1 1
 [741] 0 1 1 0 1 0 1 0 0 0 0 0 1 0 0 0 0 0 1 0 0 1 1 1 1 1 0 1 1 1 1 0 1 1 1 0 1
 [778] 0 1 1 1 0 1 1 0 0 1 1 1 0 0 1 1 1 1 0 0 1 0 1 1 1 0 0 0 0 0 1 0 1 0 0 1 0
 [815] 1 0 0 0 0 1 1 0 0 0 1 1 1 1 1 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 0 1 0 0 1
 [852] 1 0 1 0 0 1 0 0 0 0 0 1 0 0 1 0 0 1 1 0 1 1 0 0 0 1 1 1 1 0 1 1 1 0 1 1 0
 [889] 1 0 1 0 0 1 1 0 1 0 1 0 1 1 0 0 0 1 0 0 1 0 1 1 1 0 1 0 1 0 1 1 1 0 1 1 1
 [926] 1 0 0 0 1 0 1 1 1 1 1 0 0 0 1 1 0 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 1 1 1 1 0
 [963] 0 0 0 1 0 1 1 0 0 1 0 0 1 1 1 1 1 0 0 0 1 0 1 1 0 0 0 1 0 0 0 0 1 1 0 0 1
[1000] 1

The Binomial Distribution

ggplot() + 
  geom_bar(aes(x = rbinom(n = 1e6, size = 1, prob = 0.5))) + 
  theme_minimal()

Assigning our people with mutate()

assigned_group <- group_df |> 
  mutate(
    group = rbinom(1000, 1, 0.5),
    group = factor(group, labels = c("A", "B"))
  )

assigned_group
# A tibble: 1,000 × 5
      id height weight eye_colour group
   <int>  <dbl>  <dbl> <chr>      <fct>
 1     1   169.   58.8 Grey       B    
 2     2   172.  104.  Grey       B    
 3     3   173.   93.7 Grey       B    
 4     4   165.   77.6 Brown      B    
 5     5   169.   65.3 Green      B    
 6     6   161.   85.1 Grey       B    
 7     7   180.   73.4 Grey       A    
 8     8   172.   71.3 Green      B    
 9     9   167.   81.1 Green      A    
10    10   167.   75.1 Green      B    
# ℹ 990 more rows

Comparing our two groups

Comparing our two groups

Comparing our two groups